Design of Thermal Turbomachinery

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1 Institute for Thermal Turbomaschinery and Machine Dynamics Graz University of Technology Erzherzog-Johann-University Design of Thermal Turbomachinery Lecture at the Department of Aerospace Engineering Middle East Technical University Ankara, April 2008 Wolfgang Sanz Institute for Thermal Turbomachinery and Machine Dynamics Graz University of Technology Austria Content Definition of thermal turbomachinery Design details of steam turbine, gas turbine and compressors From thermodynamics to a 2D blade geometry Velocity Triangle Euler equation Efficiency definition Dimensionless parameters Blade number 3D flow and 3D blades Loss estimation Leakage flow and sealings 1

2 Definition of thermal Turbomachinery Thermal turbomachinery work with compressible fluids hydraulic machinery, ventilators Only rotating motion of the rotor and continuous flow and work process combustion engines Energy conversion is based on fluid flow: Stationary and rotating blades are used to transfer potential into kinetic energy Due to high rotational speed contact-free sealings are used piston ring in combustion engines Thus working range: large volume flows, not too high pressures Steam process Steam Water Boiler: evaporation and superheating Turbine Steam Shaft to Generator P Feed pump Water Condensator Source: Heitmeir, LN TU Graz Thermische Turbomaschinen 2

3 Steam process Dampf Eintritt: Wasserdampf Abtriebswelle zum Generator Wasser Turbine Austritt P Temperature entropy diagram Idealized process without losses Reheat cycles Peak pressure: 170 ( 300 bar, supercritical) Condensation pressure: bar (condensation) Peak temperature: C Power: MW Efficiency: 40 % (aiming at 50 % till 2020) Source:Traupel Thermische Turbomaschinen 3

Steam turbine design 20/25 MW Extraction-Condensation turbine, live steam 70 bar, 525 0 C, extraction pressure 2,6 bar,

4 Steam turbine design 20/25 MW Extraction-Condensation turbine, live steam 70 bar, C, extraction pressure 2,6 bar, Condensation pressure 0,032 bar Source: Dietzel Dampfturbinen STM 7, S. 45 Steam turbine design Source: Dietzel Dampfturbinen STM 7, S. 45 4

5 Steam turbine design Radial pump for bearing lubrication Linear guiding to allow for heat expansion Labyrinth seals Fast response bolt closes steam supply at over-speed Axial bearing (Axial thrust balancing) Source: Dietzel Dampfturbinen STM 7, S. 45 Steam turbine design Control valves Shaft rotating device Pipe for leakage flow from labyrinth seals Thermo-elastic support of stator casing Curtis stage (control stage) Live steam supply Source: Dietzel Dampfturbinen STM 7, S. 45 5

6 Siemens N-class steam turbine Siemens N-type turbines are used for normal to medium live steam conditions (100 bars, 500 C). This type of turbine has a reaction-type design that has proven itself many times over. N-type turbines can be either condensing or backpressure machines. The standard configuration allows up to two controlled extractions and/or several uncontrolled extraction points. Source: Siemens Steam turbine design GE Unterlage Site 12 Ger 3582 e Source: GE Steam turbines for STAG Combined Cycle PPlt GER3582e.pdf 6

7 Steam turbine design High pressure turbine and two-flow condensation turbine Source: GE Steam turbines for STAG Combined Cycle PPlt GER3582e.pdf Steam turbine in a nuclear plant 1200 MW turbo set with 6-flow condensation turbine Source: Siemens 7

8 Last Stage of a Condensation Turbine High pressure turbine with inner and outer casing Source: Siemens 8

Basic Principle of a Gas Turbine Fuel Exhaust gas Air Power shaft 50 70 % of turbine power to generator Compressor Turbine Pressure ratio: usually about 15, but up to 40 and more Turbine inlet

9 Basic Principle of a Gas Turbine Fuel Exhaust gas Air Power shaft % of turbine power to generator Compressor Turbine Pressure ratio: usually about 15, but up to 40 and more Turbine inlet temperature (TIT): C Turbine exit temperature (TET): C Power: 100 kw 300 MW Source: Heitmeir LN TU Graz Stationary Gas Turbine (8) Burner (7) Silo-Combustor Exit Casing Bearing (2) Turbine (4) Middle Casing (9) Transition Duct (6) Stator Blade Carrier (1) Compressor (10) Bearing (3) Inlet Casing (11) Coupling Source: Siemens 9

10 Stationary Gas Turbine Kawasaki STIG M7A-91ST Gas Turbine Source: Kawasaki 10

11 Radial Compressor Source: Pfleiderer, Strömungsmaschinen, S 310 Description of Fluid Ideal gas: p v = R T Real gas: Enthalpy-entropy-diagram 11

12 Cascade Transfer of 3D geometry to 2D linear cascade (mid section) Source: Niehuis LN Strömungsmaschinen Turbomachinery Stage Meridional View Flow channel Compressor - decreasing channel height Turbine - increasing channel height Source: Münzberg 12

13 Turbine vs. Compressor Flow Compressor - decelerating flow (diffuser) Turbine - accelerating flow (nozzle) Source: Flugzeugtriebwerke, Willy J.G. Bräunling, Radial Machine Linear cascade of a radial machine Source: Niehuis LN Strömungsmaschinen 13

14 From Thermodynamic Layout to a Turbine Cascade Steam cycle with back-pressure turbine (simplified): Power 3.13 MW Efficiency % Turbine Dh_is kj/kg mass[kg/s] p[bar] h[kj/kg] t[ C] Velocity Triangles of a Turbine Stage pressure pressure Impulse stage Reaction stage 14

15 Velocity Triangle r c = r w + r u Source: Traupel Impulse Stage vs. Reaction Stage Impulse Stage Reaction Stage - Higher turning, thus lower efficiency - Better stator and rotor efficiency - Higher enthalpy drop - Lower enthalpy drop - Rotor pressure difference small - only full admission so partial admission possible - Smaller leakage loss - Higher leakage loss (sealing at smaller radius) - Smaller axial thrust - Higher axial thrust, thus thrust balancing necessary 15

16 h-s-diagram of a Turbine Stage Total enthalpy h t0 =h t1 c 2 1 / 2 L U Total enthalpy h t2 Specific work: Stator Layout c 2 1 / 2 for the isentropic expansion: with a stator efficiency η the absolute velocity c 1 at stator exit can be obtained Using the continuity at stator exit the axial velocity component and thus the stator exit angle are obtained 16

17 Rotor Layout for the isentropic expansion: with a rotor efficiency η the relative velocity w 2 at rotor exit can be obtained Using the continuity at rotor exit the axial velocity component and thus the flow angle are obtained Specific Stage Work (Euler Equation) Axial flow at constant radius: L u = u Δc u High circumferential speed (large diameter, high rotational speed) leads to high specific work!!! 17

18 Layout for a compressor stage Axial compressor Layout for a compressor stage Radial compressor 18

19 Efficiency Definition Circumferential Efficiency, valid at mid section: Circumferential efficiency without exit loss: Circumferential efficiency with exit loss: Isentropic circumferential efficiency: Inner Efficiency Inner work: with Stator leakage loss Rotor leakage loss Wheel friction Ventilation loss Inner efficiency without exit loss: Inner efficiency with exit loss: Isentropic inner efficiency: 19

Total Efficiency η = η i η l η m η = η = i Total efficiency Inner efficiency considering all stage losses η = l Volumetric efficiency considering leakage losses of shaft η = Mechanical efficiency

20 Total Efficiency η = η i η l η m η = η = i Total efficiency Inner efficiency considering all stage losses η = l Volumetric efficiency considering leakage losses of shaft η = Mechanical efficiency considering bearing friction,... m Source: Bohl, Strömungsmaschinen 1, Seite 23 Dimensionless Stage Parameters Flow Coefficient is a dimensionless volume flow: Load Coefficient is a dimensionless enthalpy drop: In USA: c 1 =c 2 20

Degree of Reaction Definition: Isentropic

21 Degree of Reaction Definition: Isentropic enthalpy drop in rotor r = Isentropic stage enthalpy drop Kinematic degree of reaction: u 1 =u 2 Dimensionless Parameters and the Velocity Triangle r=0 r=0.5 Δc u =2u w u η su = 1 21

22 Degree of Reaction = 0 w 2 =w 3 Source: Intro. Turb. Fig 2.20 Degree of Reaction = 0.5 w 2 <w 3 Source: Intro. Turb. Fig

23 Turbines of different degree of reaction Source: Traupel 1 STM 140 Compressor Cascade Source: Traupel 1 STM

24 Compressors of different degree of reaction Source: Traupel 1 STM 140 From Thermodynamic Layout to a Turbine Cascade What is needed to design a stage? Stage enthalpy drop Rotational speed Mean diameter Degree of reaction Stator and Rotor efficiency Power 3.13 MW Efficiency % Turbine Dh_is kj/kg mass[kg/s] p[bar] h[kj/kg] t[ C]

25 Layout of a Stage Group (axial outflow) Generally: with Limit for short blades: Limit for long blades: D mean diameter n rotational speed [rpm] u circumferential velocity V volume flow α nozzle angle l blade length D i,a inner/outer diameter Number of Stages Isentropic stage enthalpy drop: h st 2 u = ψ 2 Stage number z: By varying the parameters r, ψ, α, D/l and n for the first and last stage of a stage group feasible dimensions and stage number can be found! 25

Layout of reaction stages Control stage: 20 % of turbine enthalpy drop 13 reaction

75 m 3 /s Excel Assumption of stator and rotor efficiency then allows the layout of

Blade Number Zweifel method: Zweifel investigated the ratio of the tangential force

26 Layout of reaction stages Control stage: 20 % of turbine enthalpy drop 13 reaction stages: Δh_is = 536 kj/kg V 1 = m 3 /s V 2 = 2.75 m 3 /s Excel Assumption of stator and rotor efficiency then allows the layout of the velocity triangles! Blade Number Zweifel method: Zweifel investigated the ratio of the tangential force F T to an idealised tangential force F Tid and found a common value of ψ T =0.8 F Tid ρ 2 = w2 b 2 FT ψt = F Tid w = 2 ax F = ρ w T ( w w ) 2u 2 2 w 1u ax t b ( w w ) 2u 1u t (5) 26

27 Zweifel method: Blade Number With ψ T =0.8 an optimum ratio between spacing t and blade width b can be found! ψ = 0,8 T t b opt 2 0,8 w2 = 2 w Δw ax u t b opt 0,8 sin = 2 sin β sin 2 β1 0,8 1 = 2 ( β β ) 2 sin β ( cot β cot β ) For compressible flows: t b opt Δρ = 0,8 ρ w Δw 2 ax2 u with Δp=p 1t -p 2 The blade width b can be chosen or is given by strength considerations! Blade Number Alternatively following diagram by Traupel can be used to find the optimum spacing depending on the blade turning: Source: Traupel I,

28 Next Step: Blade Geometry Based on the velocity triangle the blade geometry is designed The flow channel should allow a continuous acceleration (or deceleration) The narrowest area (throat) is usually at the blade trailing edge! Source: Bild 6.1 STM 152 Japikse Introduction into Turbomachinery Examples for Blade Design based on Zweifel method 28

29 Method of Traupel: Does the flow follow the geometry? Continuity: Impulse in circumferential direction: Method of Traupel a c a 2 sinα2 = = t c2 t cosαa a cosα Thus Daher the wird blade der Abströmwinkel exit flow angle als depends Funktion on der theteilung throatder areaminimal and the throat Öffnung flow und angle des Strömungswinkels an dieser Stelle erhalten. 1 a tanα 2 = cosα t Considering the thickness of the blade trailing edge, following formula is obtained: 1 a tgα 2 = cosα t τ a a The blade geometry has to be adapted so that α 2 corresponds to the velocity triangle. 29

pressure gradients lead to vortices Mach number distribution along suction and pressure side of a

30 Turbomachinery Flow Flow in turbomachinery is very complex: three-dimensional laminar, transitiónal or turbulent unsteady with stator-rotor interaction transonic with shock boundary layer interaction high pressure gradients lead to vortices Mach number distribution along suction and pressure side of a turbine at subsonic and transonic conditions Instantaneous pressure distribution in a transonic turbine 30

31 Three-dimensional Blade Design Until now the blade geometry was determined only for a representative mid section. But there are differences along the blade height: The circumferential velocities vary along the blade height. The radial balance between centrifugal and pressure forces leads to a radial pressure distribution. This leads to different velocity triangles along the blade height and thus a twist of the 3D blade is necessary (except for very small D/l ratios) Three-dimensional Force Balance Stream line in a meridional channel without blades: Force Balance in x-direction: Force Balance in y-direction: d a... centrifugal force by circumferential velocity b... centrifugal force by streamline curvature c... pressure force d... convective force 31

32 Three-dimensional Force Balance Some transformations and the assumption of isentropic flow lead to: Assumption of no curvature and parallel-to-axis flow lead to: Assumption of the same enthalpy drop along the radius: Constant Nozzle Angle Design Postulation of a constant nozzle exit angle: Effective in the axial gap between stator and rotor 32

33 Constant Nozzle Angle Design Starting point is the velocity triangle at mid section: 3. The constant specific work at all radii gives the relative outlet velocities! 4. u gives the absolute outlet velocities! Only rotor blade is twisted! The same exit angle and thus the same blade geometry for all sections! 2. Circumferential velocity u gives the relative inlet velocities! 1. The cosα law gives the absolute velocity c for all radial sections! Constant Nozzle Angle Design Specific volume v out mid in Kinematic degree of reaction Mass flow Stator enthalpy drop 33

34 Free-Vortex Design Postulation of a constant axial velocity between stator and rotor: 3D layout of a fan stage: Rotor and stator blade are twisted! Three-dimensional Blade Design The linear forced vortex law reduces the turning at the blade hub, the quadratic forced vortex law also reduces the turning at the blade tip. This results in a decrease of secondary losses! Variation of nozzle exit angle across the annulus for various vortex designs Source: Fig 6.1 STM 152 Japikse Introduction into Turbomachinery 34

35 Secondary Flows Secondary flow with tip leakage vortex Separating surface Passage vortex (casing) Tip leakage vortex Inlet flow Casing Wall Suction side Trailing edge vortex Passage vortex Corner vortex Hub wall side-wall flow Corner vortex Suction side leg of the horse-shoe vortex Passage vortex (hub) Secondary flow in turbines Hp Pressure side leg of the horse-shoe vortex Hs Suction side leg of the horse-shoe vortex Modern 3D Blade geometry Where do the highest secondary losses occur? Stacking of two-dimensional sections along radius Source: Fig. 6.1 STM 152 Japikse Introduction into Turbomachinery 35

36 Modern 3D Blade geometry Source: BWK 3/2005, Seite 58, Bild 3 Modern 3D Blade geometry Meridian stream lines High mass flow density Cylindrical stator blades Low mass flow density Bowed stator blades Source: BWK 3/2005, Seite 60, Bild 4 36

influence Mach number influence Trailing edge influence Trailing edge influence Circumferential

37 GE-90 3D Fan Blade Design Source: GE Loss Calculation by Traupel Stator/rotor efficiency: Profile loss Side wall friction Additional losses Basic profile loss due to flow turning Mach number influence Mach number influence Trailing edge influence Trailing edge influence Circumferential efficiency: Inner efficiency: Stator leakage loss Stator leakage loss Wheel friction loss Ventilation loss 37

38 Tip leakage loss by Jericha leakage efficiency s leakage height l blade height l s blade chord length Part Load Operation Loss coefficent Impulse turbine Reaction turbine Incidence Losses of impulse and reaction turbine dependent on the incidence angle (Dietrichs et al, 1987) Source: Dietrichs et al.,

Lowest leakage loss Lowest leakage loss Flow through sealings

39 Labyrinth seals Steam turbine Labyrinth seals to prevent steam leakage Different sealing designs Relative leakage flow Lowest leakage loss Lowest leakage loss Flow through sealings is a repeated throttle flow Source: BWK 3/2005, Seite 60, Bild 6 39

Estimate of sealing mass flow Estimation of sealing gap height: [mm] with k = 0.

3 for turbines with an austenitic runner Estimation of sealing mass flow (simplified):

volume before first seal z number of seal spikes Φ flow coefficient, depending on

40 Estimate of sealing mass flow Estimation of sealing gap height: [mm] with k = 0.6 for compressor k=0.85 for turbines with a ferritic runner k=1.3 for turbines with an austenitic runner Estimation of sealing mass flow (simplified): A gap area p 1 pressure before first seal p 2 pressure after last seal v 1 specific volume before first seal z number of seal spikes Φ flow coefficient, depending on sealing geometry Abradable Coatings Abradable coatings allow a reduced clearance Source: BWK 3/2005, Seite 61, Bild 7 40

41 Brush Sealings Brush sealings allow a further clearance reduction Source: BWK 3/2005, Seite 62, Bild 8 Axial Thrust Balancing Example of a steam turbine with control stage: Balance piston allows balancing of axial forces 41

Alpha College of Engineering

Alpha College of Engineering Department of Mechanical Engineering TURBO MACHINE (10ME56) QUESTION BANK PART-A UNIT-1 1. Define a turbomahcine. Write a schematic diagram showing principal parts of a turbo